Cardiac Pacing and ICDs - Fourth Edition pptx

For the vast majority of cases with incident velocity f0.99c down to about thespeed of a least-bound electron, the dominant energy transfer mechanism is by electrosta-tic and electromagn

Charged Particle and Photon

C he mi c a I, Physic oc h emi c a I, a nd B iolog i ca I

Consequences with Applications

University of Notre Dame

Notre Dame, Indiana, U S A

Although great care has been taken to provide accurate and current information, neither the author(s)nor the publisher, nor anyone else associated with this publication, shall be liable for any loss, damage,

or liability directly or indirectly caused or alleged to be caused by this book The material containedherein is not intended to provide specific advice or recommendations for any specific situation.Trademark notice: Product or corporate names may be trademarks or registered trademarks and areused only for identification and explanation without intent to infringe

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The purpose of this work is to present a coherent account of high-energy charged particleand photon interactions with matter, in vivo and in vitro, that will be of use to both studentsand practicing scientists and engineers The book encompasses not only radiation chemis-try and photochemistry, but also other aspects of charged particle and photon interactions,such as radiation physics, radiation biochemistry, radiation biology, and applications tomedical and engineering sciences and to radiation synthesis and processing and foodirradiation Any phenomenon of ionization and excitation induced by charged particleand photon interactions with matter is considered of interest, since information on theinteractions of photons with matter help us understand the interactions of charged particleswith matter Further, the study of the interactions of high-energy photons, particularly inthe vacuum ultraviolet–soft X-ray (VUV-SX) region, is of great importance in bridging thearea between photochemistry and radiation chemistry (see Chapter 5) Throughout thebook a major aim has been to elucidate the physical and chemical principles involved inapplications of significance to practicing scientists and engineers We have secured theforemost workers in their respective areas to contribute chapter articles in a manner thatensures contact with adjacent disciplines, keeping in mind the needs of the general reader-ship

Since its inception, radiation effects have had ramifications in various fields, whichsometimes use different technical language, units, etc Reviews condense the subject matterwhile amplifying important points and bring these up-to-date for students and researchers

In a field that is developing as rapidly as radiation effects in vivo and in vitro, there is a needfor periodic summaries in the form of a book In the present millenium, a great need hasdeveloped for in-depth studies with a balance of experiment, theory, and application Yet,chapters written by several authors in the same book may use different styles, outlooks, oreven notations We have paid particular attention to these factors and have striven to makethe presentations uniform

By its very nature this book is interdisciplinary The first eleven chapters delineate thefundamentals of radiation physics and radiation chemistry that are common to all irra-diation effects.Chapters 12and13deal with specific liquid systems, whileChapter 14 isconcerned with LET effects.Chapters 15to18describe biological and medical consequences

of photon and charged-particle irradiation The rest of the book is much more applied incharacter, starting with irradiated polymers inChapter 19and ending with applications ofheavy ion impact inChapter 27

Our aim has been to provide a self-contained volume with sufficient information anddiscussion to take the reader to the frontier of investigation The level of presentation is atthe advanced undergraduate level, so that undergraduates, graduate students, researchers,

and practicing professionals may all benefit from it It is assumed that the reader has someknowledge of chemistry or biology or physics but is not necessarily versed in the properties

of high-energy radiation

It is our pleasure and privilege to thank our friends and colleagues all over the worldwho have contributed to our understanding of the high-energy charged particle and photoninteractions with matter

A Mozumder

Y Hatano

Charged ParticlesLarry H ToburenChapter 4 Modeling of Physicochemical and Chemical Processes

in the Interactions of Fast Charged Particles with MatterSimon M Pimblott and A Mozumder

Chapter 5 Interaction of Photons with Molecules: Photoabsorption,

Photoionization, and Photodissociation Cross SectionsNoriyuki Kouchi and Y Hatano

Chapter 6 Reactions of Low-Energy Electrons, Ions, Excited Atoms

and Molecules, and Free Radicals in the Gas Phase as Studied byPulse Radiolysis Methods

Masatoshi Ukai and Y HatanoChapter 7 Studies of Solvation Using Electrons and Anions in

Alcohol SolutionsCharles D JonahChapter 8 Electrons in Nonpolar Liquids

Richard A HolroydChapter 9 Interactions of Low-Energy Electrons with Atomic and

Molecular SolidsAndrew D Bass and Le´on Sanche

Chapter 10 Electron–Ion Recombination in Condensed Matter:

Geminate and Bulk Recombination ProcessesMariusz Wojcik, M Tachiya, S Tagawa, and Y HatanoChapter 11 Radical Ions in Liquids

Ilya A Shkrob and Myran C Sauer, Jr

Chapter 12 The Radiation Chemistry of Liquid Water: Principles and

Applications

G V BuxtonChapter 13 Photochemistry and Radiation Chemistry of Liquid Alkanes:

Formation and Decay of Low-Energy Excited States

L WojnarovitsChapter 14 Radiation Chemical Effects of Heavy Ions

Jay A LaVerneChapter 15 DNA Damage Dictates the Biological Consequences of

Ionizing Irradiation: The Chemical PathwaysWilliam A Bernhard and David M CloseChapter 16 Photon-Induced Biological Consequences

Katsumi KobayashiChapter 17 Track Structure Studies of Biological Systems

Hooshang Nikjoo and Shuzo UeharaChapter 18 Microdosimetry and Its Medical Applications

Marco Zaider and John F DicelloChapter 19 Charged Particle and Photon-Induced Reactions in Polymers

S Tagawa, S Seki, and T KozawaChapter 20 Charged Particle and Photon Interactions in Metal Clusters

and Photographic System StudiesJacqueline Belloni and Mehran MostafaviChapter 21 Application of Radiation Chemical Reactions to the Molecular

Design of Functional Organic MaterialsTsuneki Ichikawa

Chapter 22 Applications to Reaction Mechanism Studies of Organic

SystemsTetsuro MajimaChapter 23 Application of Radiation Chemistry to Nuclear Technology

Yosuke Katsumura

Chapter 24 Electron Beam Applications to Flue Gas Treatment

Hideki NambaChapter 25 Ion-Beam Therapy: Rationale, Achievements, and

ExpectationsAndre´ Wambersie, John Gueulette, Dan T L Jones, andReinhard Gahbauer

Chapter 26 Food Irradiation

Jo´zsef FarkasChapter 27 New Applications of Ion Beams to Material, Space, and

Biological Science and EngineeringMitsuhiro Fukuda, Hisayoshi Itoh, Takeshi Ohshima,Masahiro Saidoh, and Atsushi Tanaka

Andrew D Bass University of Sherbrooke, Sherbrooke, Que´bec, Canada

Jacqueline Belloni UMR CNRS–UPS, Universite´ Paris-Sud, Orsay, France

William A Bernhard University of Rochester, Rochester, New York, U.S.A

G V Buxton University of Leeds, Leeds, England

David M Close East Tennessee State University, Johnson City, Tennessee, U.S.A.John F Dicello Johns Hopkins University School of Medicine, Baltimore, Maryland,U.S.A

Jo´zsef Farkas Szent Istva´n University, Budapest, Hungary

Mitsuhiro Fukuda Japan Atomic Energy Research Institute, Takasaki, Gunma, JapanReinhard Gahbauer Ohio State University, Columbus, Ohio, U.S.A

John Gueulette Universite´ Catholique de Louvain, Brussels, Belgium

Y Hatano Tokyo Institute of Technology, Tokyo, Japan

Richard A Holroyd Brookhaven National Laboratory, Upton, New York, U.S.A.Tsuneki Ichikawa Hokkaido University, Sapporo, Japan

Hisayoshi Itoh Japan Atomic Energy Research Institute, Takasaki, Gunma, JapanCharles D Jonah Argonne National Laboratory, Argonne, Illinois, U.S.A

Dan T L Jones iThemba Laboratory for Accelerator Based Sciences, Somerset West,South Africa

Yosuke Katsumura The University of Tokyo, Tokyo, Japan

Katsumi Kobayashi High Energy Accelerator Research Organization, Tsukuba, JapanNoriyuki Kouchi Tokyo Institute of Technology, Tokyo, Japan

T Kozawa Osaka University, Osaka, Japan

Jay A LaVerne University of Notre Dame, Notre Dame, Indiana, U.S.A

Tetsuro Majima Osaka University, Osaka, Japan

Mehran Mostafavi UMR CNRS–UPS, Universite´ Paris-Sud, Orsay, France

A Mozumder University of Notre Dame, Notre Dame, Indiana, U.S.A

Hideki Namba Japan Atomic Energy Research Institute, Takasaki, Gunma, JapanHooshang Nikjoo Medical Research Council, Harwell, Oxfordshire, England

Takeshi Ohshima Japan Atomic Energy Research Institute, Takasaki, Gunma, JapanSimon M Pimblott University of Notre Dame, Notre Dame, Indiana, U.S.A

Masahiro Saidoh Japan Atomic Energy Research Institute, Takasaki, Gunma, JapanLe´on Sanche* University of Sherbrooke, Sherbrooke, Que´bec, Canada

Myran C Sauer, Jr Argonne National Laboratory, Argonne, Illinois, U.S.A

S Seki Osaka University, Osaka, Japan

IIya A Shkrob Argonne National Laboratory, Argonne, Illinois, U.S.A

M Tachiya National Institute of Advanced Industrial Science and Technology (AIST),Tsukuba, Japan

S Tagawa Osaka University, Osaka, Japan

Atsushi Tanaka Japan Atomic Energy Research Institute, Takasaki, Gunma, JapanLarry H Toburen East Carolina University, Greenville, North Carolina, U.S.A.Shuzo Uehara Kyushu University, Fukuoka, Japan

Masatoshi Ukai Tokyo University of Agriculture and Technology, Tokyo, JapanAndre´ Wambersie Universite´ Catholique de Louvain, Brussels, Belgium

Mariusz Wojcik Technical University of Lodz, Lodz, Poland

L Wojnarovits Hungarian Academy of Sciences, Budapest, Hungary

Marco Zaider Memorial Sloan-Kettering Cancer Center, New York, New York,U.S.A

* Canada Chair in the Radiation Sciences

In the 18th century the action of light on silver salts was definitely established, culminating

in rudimentary photography in the mid-19th century (seeChapter 20).Some qualitativeunderstanding of photochemical action was obtained by Grottus (1817) and by Draper(1841) in which it was stated that only the absorbed light can be effective in bringingout chemical transformation and that the rate of chemical change should be proportional

to the light intensity With the advent of the quantum theory, Einstein (1912) formalizedwhat has since been called the first law of photochemistry, i.e., only one quantum of light isabsorbed per reacting molecule This actually applies to the primary process and atrelatively low light intensity to which all early studies were confined Later work at highintensity provided by lasers has necessitated some modification of this important law

As not all primary activations are observable, the idea of the quantum yield or the number

of molecules transformed per quantum of light absorbed was introduced by Bodenstein(1913) who also noticed chain reactions in the combination of hydrogen and chlorinegiving quantum yields many orders of magnitude greater than 1

It is clear that, along with the discovery of x-rays in 1895, Roentgen also found thechemical action of ionizing radiation He drew attention to the similarity of the photo-graphic effect induced by light and x-rays Application to medicine appeared very quickly,followed by industrial applications However, this field of investigation remained namelessuntil Milton Burton, in 1942, christened it‘‘radiation chemistry’’ to separate it from radio-chemistry which is the study of radioactive nuclei Historical and classical work in radia-tion chemistry has been reviewed by Mozumder elsewhere [1] Here we will only make afew brief remarks

Lind [2] has defined radiation chemistry as the science of the chemical effects broughtabout by the absorption of ionizing radiation in matter It should be distinguished fromradiation damage which refers to structural transformation induced by irradiation, par-ticularly in the solid state The distinction is not always maintained, perhaps uncon-sciously, and sometimes both effects may be present simultaneously Following asuggestion of M Curie around 1910, that ions were responsible for the chemical effects

of radioactive radiations, the symbol M/N was introduced to quantify the radiationchemical effect, where M is the number of molecules transformed (created or destroyed)and N is the number of ion pairs formed Later, Burton [3] and others advocated thenotation G for the number of species produced or destroyed per 100 eV (=1.602
1017J)absorption of ionizing radiation It was purposely defined as a purely experimentalquantity independent of implied mechanism or assumed theory

Bethe [4] first pointed to the quantitative similarity of the excitation of a molecule bylight and by fast charged particle impact, thereby underscoring the importance of dipoleoscillator strength Despite modifications required for slower charged particles, this opticalapproximation(see Sec 3 andChapters 2and5)remains a cornerstone in the understanding

of the primary processes in radiation chemistry In the totality of the various effects broughtabout by irradiation, the radiation chemical effects occupy a central position In a similarfashion electrons and photons are the most important agencies for bringing the radiationeffects Electrons are always produced as secondary irradiation irrespective of the nature ofthe primary ionizing particle Photons are ubiquitous and, in any case, understanding ofcharged particle impact requires a knowledge of photon impact processes

Generally speaking, industrial applications of irradiation have a relatively short tory except for some medical applications The field, however, has gained considerablemomentum since the 1960s Spinks and Woods [5] have summarized radiation-inducedsynthesis and processing; Mozumder [1] has also given a brief account of various appli-cations to science and industry including dosimetry, food irradiation, waste treatment,sterilization of medical equipment, etc Salient features of radiation chemistry, both in thegaseous and condensed phases, have been discussed in the CRC Handbook of RadiationChemistryedited by Tabata et al [6] Special topics of the interactions of excess electrons indielectric media have been adequately reviewed in a CRC handbook edited by Ferradiniand Jay-Gerin [7] Further, specific applications to atomic and molecular processes inreactive plasmas have been summarized by Hatano [8].Chapters 15through27of this bookare involved with radiation applications including radiobiological, medical, and industrialapplications In addition,Chapters 16,19,and20discuss, in considerable details, the effectsand applications of photon irradiation An important role of synchrotron radiation (SR) as

his-a new photon source whis-as theoretichis-ally pointed out for the first time his-about 40 yehis-ars his-ago byR.L Platzman and U Fano Recent progress in SR research has been remarkable, asreviewed by Hatano elsewhere [9] See also Chapter 5 for the newly established dedicated

SR facilities combined with new experimental methods for spectroscopy and dynamics

2 TIME SCALE OF RADIATION ACTION

In the action of charged particle and photon irradiation on condensed matter, it is structive to consider several stages of overlapping time scales The stages, in ascendingorders of time, are called the physical, physicochemical, and chemical stages, respectively,for radiation chemical studies To these, biochemical and biological stages have been addedfor application to radiobiology [10,11] Within each stage various events take placeoccupying their respective time scales For example, within the biochemical stage (f103

in-to f10 sec), secondary radicals form, evolve, and react, while the biological stage covers

a wide range of time from mitosis to late biological effect The earliest discernible time, in thephysical stage, is obtained from the uncertainty principle, DEDtf,, as f1017

sec, whichcorresponds to the production of secondary electrons with energyz100 eV Times such asthese or shorter are just computed values The longest time scale in radiobiology may exceedseveral years or generations if genetic effects are included Morrison [12] first gave anapproximate time scale of events for application to radiobiology Several authors haveperiodically updated the concept for different types of application More recently, Lentleand Singh [10] and Mozumder [11] have discussed this topic from the points of view ofradiation biology and radiation chemistry, respectively

Table 1 summarizes some of the events that occur through the various stages Ithas been suggested that, following ionization in liquid water, the ‘‘dry’’ hole H2O+can

Water

energy loss to fast secondaryelectrons

(Vertical excitation)

H and OH formed

Longitudinal dielectric relaxation

in water Molecular vibration

Fast dissociation

Spur formed Self-diffusion timescales in simple liquids

time in water

low viscosity Secondary reactionsincluding intertrack reactions

media Intratrack reactionscompleted Secondary radicalformation and reaction

Biochemical effects

very high viscosity Time for mitosis

Biochemical effects of metastables

DNA synthesis timeBiological effectsLate biological effects

move by exact resonance until the ion-molecule reaction H2O +H2O!H3O +OHlocalizes the hole The earliest chemical transformation, indicated by H-atom transfer inreactions of the type ROH++ROH!ROHþ

2+RO, then occurs in f1014 sec in waterand alcohols [13] The time needed for electron hydration is theoretically computed to bef0.2 psec [14] while experiment gives an upper limit of 0.3 psec [15] The informationpresented inTable 1is not to be taken too literally Each stage may contain many orders ofmagnitude of time, but the usefulness of the time scale picture rests on the perception thatwithin an order of magnitude relatively few processes compete As the species that exist atthe end of one stage serve as the input to the next stage, the qualification‘‘early’’ is relative

In radiobiological systems, the time of appearance of a change may be subjective depending

on the cell cycle, which is due to several different kinds of generations of biochemical andbiological transformations that must take place to render the radiation-induced transfor-mation‘‘visible.’’ Also, these processes can occur both in the directions of repair and ampli-fication Certain biochemical reactions, for example, that of OH with sugars, may occur inthe nanosecond time scale while others, such as those giving the O2effect, may take micro-seconds DNA strand breakage may be considered an early biological effect while otherdamages can take f1 day to f40 years when genetic effects are considered This should becontrasted with f1Asec needed for track dissolution in liquid water [16]

In the current millennium there is a strong need for interdisciplinary research ing an integrated outlook In this sense various disciplines connected with radiation actionall start with radiation physics and radiation chemistry From that point on one sees abifurcation One way goes to radiation biochemistry to radiation biology and to medicalapplications Another way goes to engineering and industrial applications including, butnot limited to, polymerization, waste management, food preservation, etc

involv-3 FUNDAMENTAL PROCESSES IN THE PHYSICAL, PHYSICO-CHEMICAL,AND CHEMICAL STAGES OF INTERACTIONS OF HIGH-ENERGY

CHARGED PARTICLES AND PHOTONS WITH MATTER

In the interactions of high-energy incident particles, i.e., photons, electrons, heavy chargedparticles (or positive and negative ions), and other particles, with matter, the succession ofevents that follow the absorption of their energies has been classified into three character-istic temporal stages: physical, physico-chemical, and chemical stages [17] (see Sec 2) Thephysical stage consists of the primary activation of molecules in matter (in the case, forexample, it is composed of molecular compounds), due to the collision of high-energyincident particles to form electronically excited or ionized states of molecules and ejectedelectrons The electrons thus formed may have sufficient energy to further ionize the sur-rounding molecules At the end of the interactions, electrons are formed in a wide energyrange via cascading electron–molecule collision processes These secondary electrons fur-ther decrease their energies to the subexcitation energy range, leading to the formation ofreactive species, i.e., ions, excited molecules, free radicals, and low-energy electrons Thesespecies interact with each other or with stable molecules Subexcitation electrons, whichare electrons below the first excitation potential, degrade their energies by vibrational,rotational, and/or elastic collisions to reach thermal energy Electrons in the thermal andepithermal ranges disappear predominantly by recombination, attachment, or diffusion It

is concluded therefore that a decisive step in the physical and physico-chemical stages ofthe interactions of high-energy incident particles with matter is the collision of secondaryelectrons with molecules in a wide energy range (see Chapters 2– , 9, 17) The entirefeature of the fundamental processes of the interactions of high-energy incident particles

with molecules, i.e., the molecular processes in the physical and physico-chemical stages(and further, the chemical stage which mainly consists of free radical reactions), are sum-marized in Table 2 [18] (seeChapter 6).

Table 2 shows that molecules AB in collisions with electrons in a wide energy rangeare directly ionized and excited into superexcited states [9] above their first ionizationpotentials (IP) and into excited states below IP Superexcited states ABV are competitivelyautoionized or dissociated into neutral fragments, i.e., free radicals or stable productmolecules (seeChapter 5).Electronically excited states AB* are also dissociated to neutralfragments Parent ions directly formed via ionization, or indirectly via autoionization, arecollisionally (and/or unimolecularly) stabilized or dissociated into fragment ions Suchions, particularly in the condensed phase, may be quickly neutralized with electrons bygeminate recombination or competitively converted to other ions via ion–molecule re-actions (see Chapter 6), while in the gas phase such conversion is predominant comparedwith recombination, depending on the pressure In case of the addition of electronegativesolute molecules, negative ions are produced in electron attachment processes Electronswith characteristic energies are selectively captured by molecules to form negative ions (seeChapter 6) It is generally accepted that molecular clusters, large aggregates of molecules,and molecules in the condensed phase can capture electrons with large cross sections due

to electron attachment dynamics different from those in the gas phase for isolated singlemolecules [19,20] For polar molecules, electrons or ions are solvated with molecules toform solvated electrons and ions, respectively (see Chapter 7) The recombination ofpositive ions with electrons, particularly in the condensed phase, is classified as geminateand bulk recombination processes (seeChapter 10) A relative importance of these twoprocesses is closely related with the transport mechanism of electrons in it, i.e., the mag-

and Chemical Stages of the Interactions of High-Energy Charged

Particles and Photons with Molecules AB

nitudes of the electron drift mobility or the electron conduction band energy in it nomenologically, it is more dependent on the properties of the medium molecules (seeChapter 8).In some cases, particularly in admixed systems both in the gas and condensedphases, energy or charge transfer processes may predominantly occur from molecules ofthe major component in the system to added solute molecules (see Chapter 6).

Phe-As described above, a crucial step of the physical and physicochemical stages is thecollision of secondary electrons with molecules in a wide energy range Therefore the infor-mation on electron–molecule collision cross-section data, which must be correct, absolute,and comprehensive, is of great importance and is helpful for understanding the essentialfeatures of the fundamental processes in these two stages [21] Such information is avail-able both experimentally and theoretically in the gas-phase (see Chapter 3),but in somecases also in the condensed-phase as well (seeChapter 9) Cross sections for the ionizationand excitation of molecules in collisions with electrons in the energy range greater thanabout 102eV are well elucidated quantitatively by the Born–Bethe theory [22] This theory

is also helpful for calculating, at least roughly, these cross-section values further in thelower energy range

According to the optical approximation, which was shown by Platzman [23] to bebased on the Born–Bethe theory, a radiation chemical yield G may be estimated from opticaldata, viz., photoabsorption cross sections, oscillator strength distributions, photoionizationcross sections, and photodissociation cross sections of molecules in a wide range of thephoton energy or wavelength, particularly in VUV–SX region [9] (seeChapter 5).Basically,this approximation should be applied only for a rough estimation of G values Such alimitation may be attributed to a superficial comparison of radiation chemical yields foratomic systems with electron- atom cross-section data in a limited collision-energy rangewhich were available in earlier stages of the related research fields in the 1960s Recently,however, its applicability has been examined by comparing electron-collision cross sectionsfor molecules in a wide collision energy range between optically allowed and forbiddentransitions, providing the conclusion, at least tentatively, that this approximation may beapplicable to the estimation of G values more precisely than previously considered [24].There is a great need to examine the applicability more systematically because of recentprogress in the experimental and theoretical investigations of electron–molecule collisionprocesses [21]

The experimental and theoretical investigations of the physical, physico-chemical,and chemical stages of the interactions of high-energy incident particles with matter havemade a remarkable contribution to recent progress in fundamental studies of the static anddynamic behavior of reactive species, i.e., electrons, ions, excited atoms and molecules, andfree radicals Conversely, these are needed for a comprehensive understanding of recentprogress in the fundamental studies of reactive species, where a scientifically reasonableanalysis of the interesting but complex mechanism of the interactions of high-energy inci-dent particles with matter is involved Thus it often provides new findings of reactive species

as well as their static or dynamic behavior For that purpose, the matrix representation ishelpful for summarizing or surveying the diverse information on such fundamental studies

of a variety of reactive species [18]

4 FIELDS OF STUDY: RELEVANCE TO BASIC AND APPLIED SCIENCESThe fields of study undertaken in the present book are rather broad However, the con-tributors, recognized experts in their respective areas, have striven to ensure continuity by

connecting important concepts to adjacent areas Thus, in one example, the logical flowwould be from physics to chemistry to biology and medicine, and in another example itcould be from physics to chemistry to industrial applications, including polymerization,waste, and flue-gas treatment, etc In choosing the subject matters it has been the objective

of the editors that comparable importance is given to fundamentals and applications.While it has been well recognized by almost everyone that radiation effect starts with aphysical interaction, very often followed by chemical reactions, etc., the chemical stage issometimes understressed in radiobiological discussions [25] In a similar vein, the appliedradiation scientist may have a right to think that aqueous radiation chemistry has beenoverstressed by the physical chemists who claim it to be a better understood topic inchemical kinetics [26] In any case the editors have taken care so that each significant area

of investigation would receive comparable attention

Studies in radiation science and technology may be viewed from three angles,namely, life, industry, and basic knowledge According to some estimates [27], thecontinual exposure to environmental radiation over geological periods is important andmust be taken into account There is now a widespread belief that aging and, indeed, thegenetic evolution of man may be significantly influenced by ambient radiation Under-standing of these effects duly belongs to radiation biology, which depends on radiationphysics and radiation chemistry for basic information Radiation is applied in industry invarious ways—for example, as reaction initiators, sustainers, and also as control mech-anisms Some of the important ones are included in this book, while others, such as curing

of paints, materials for textile finishing, applications in mining and metallurgy, etc., are leftout for obvious space limitation Finally, the important contribution made by radiationchemistry to experimental basic science should be appreciated in making availableexcitations to states which would otherwise be inaccessible by thermal activation

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Wiley-Inter-science: New York, 1991

Raton, 1991

Raton, 1991

Systems; In Nickson, J.J., Ed.; Wiley: New York, 1952; 1–12

Rodgers, M.A.J., Eds.; Chap 5 VCH Publishers: New York, NY, 1987

Res 1983, 96, 437

17 Platzman, R.L Vortex 1962, 23, 327.

Press: Boca Raton, 1991

J.R., Eds.; Elsevier: Amsterdam, 1986; 153 pp

IAEA-TECDOC-799 IAEA: Vienna, 1995

1956

Princeton, 1961

Russian); Daniel Davey: New York, 1964

Interaction of Fast Charged Particles

with Matter

A Mozumder

University of Notre Dame, Notre Dame, Indiana, U.S.A

1 ENERGY TRANSFER FROM FAST CHARGED PARTICLES

1.1 General Features

Any momentum change of an incident particle constitutes a collision In the interaction of

an incident particle with an atom or a molecule, the collisions are classified as elastic orinelastic In elastic collisions, energy and momentum are conserved between the externaldegrees of freedom (e.g., translation) of the colliding partners In inelastic collisions, en-ergy is transferred into, or from, the internal degrees of freedom of the struck molecule,designated as collisions of the first and the second kind, respectively Because collisions ofthe second kind are important for epithermal and thermal particles alone, we will only beconcerned with the collisions of the first kind in this chapter Furthermore, akin to theGrottus principle (see the Introduction) in photochemistry, only the energy absorbed by amolecule can bring about radiation–chemical change, or the ensuing radiobiological trans-formation Therefore the internal molecular excitation (electronic, vibrational, etc.) is anecessary precursor of radiation-induced transformation In this context, ionization is in-cluded as an extreme form of electronic excitation

Particles and waves are distinguished only in classical mechanics In quantum chanics they are interchangeable, giving rise to first and second quantizations, respectively.However, it is customary to group the incident radiations as light (electrons, muons, x-and g-rays, etc.) or heavy (protons, a-particles, fission fragments, etc.) particles Photons,classified as a separate group, can cause excitation and ionization in a molecule Ionization

me-by photons can proceed me-by any of the three following mechanisms: photoelectric effect,Compton effect, and pair production In the photoelectric effect, the photon is absorbed andthe emergent electron inherits the photon energy reduced by the sum of the binding energy

of the electron and any residual energy left in the resultant positive ion (Einstein equation)

In the Compton effect, the photon is scattered with significantly lower energy by a mediumelectron, which is then ejected with the energy difference In the pair production process,the photon is annihilated in a nuclear interaction, giving rise to an electron–positron pair,which together carries the photon energy lessened by twice the rest energy of the electron.This process therefore has an energetic threshold With increase in photon energy, thedominant interaction changes from photoelectric to Compton to pair production For

Co-g rays, almost the entire interaction is induced by the Compton effect which, by theKlein–Nishina theory, gives a nearly flat electron energy spectrum Thus the 1.2-MeVphoton generates a wide spectrum of Compton electrons having an average energy off0.6 MeV; consequently, the medium molecules respond as if being showered by thesefast electrons Pair production is a characteristic of very high energy photons; again, to themedium molecules, the effect is the same as a spectrum of fast electrons and positrons ofappropriate energy Electrons of various energy are the most important sources as primaryradiations in the laboratory and in the industry [1], and also as secondary radiations in anyform of ionizing event Other often-used irradiations include x-rays, radioactive radiations(a, h, or g), protons, deuterons, various accelerated stripped nuclei, and fission fragments.X-rays differ from g-rays operationally, i.e., x-rays are generated by machines whereas g-rays are produced in nuclear transformations.

At ultrarelativistic speeds (vfc, the speed of light), a radiative process, called thenuclear bremsstralung, becomes significant Bethe and Heitler [2] estimated the ratio ofenergy losses of a charged particle due to radiative (bremsstralung) and collisional (elec-tronic) processes at an energy of E MeV approximately as EZ/800, where Z is the nuclearcharge For electrons in water, this radiative process only becomes significant above 100MeV For the vast majority of cases with incident velocity f0.99c down to about thespeed of a least-bound electron, the dominant energy transfer mechanism is by electrosta-tic and electromagnetic interactions between the incident charged particle and the mediumelectrons Of these, the electromagnetic interaction becomes important only at relativisticspeeds [3] Therefore in most cases of importance to radiation science, the principalinteraction of an incident-charged particle with the medium electrons is of electrostaticorigin

For fast charged particles impinging on matter, the very first discernible effect is theelectronic excitation of molecules or atoms Because electron is the lightest particle, itsexcitation occurs at the earliest time scale consistent with the uncertainty principle, i.e., inf1016sec Later, transformation of the deposited energy in the various internal degrees

of freedom occurs in their respective time scale, e.g., inf1012sec for vibration, etc Somedetails were presented elsewhere [4] Molecular dissociation and low-grade heat appear atlonger time scales and, in some cases involving exothermal reactions, the level of low gradeheat can terminate above that of absorbed electronic energy There is no evidence of localrise of temperature for fast incident charged particles

1.2 Radiation Physics and Radiation Chemistry

Although in nature there is no distinction between physical and chemical effects, inpractice it is profitable, depending on the investigator’s choice of discipline, to view theradiation effect either from the point of view of the incident particle or from that of themedium molecules, designated as radiation physics and radiation chemistry, respectively.Thus the study of the charge, rate of energy loss, range, and penetration, etc of theincident particle, any of which may change under the interaction, constitutes radiationphysics Study of the matter receiving the absorbed energy to produce chemical changes,charge separation, luminescence, etc essentially belong to radiation chemistry It is evidentthat radiation chemistry is the link between radiation physics and radiation biology (see

Ch 1, Sec 2) Some investigators recognize this link explicitly [5,6], while others shortcircuit the chemical part, working directly from the physics of energy deposition tobiological effects [7] That necessitates the introduction of additional parameters, such as acritical dose or concepts such as microdosimetry [8,9]

1.3 Condensed Matter: Localization of Deposited Energy

Fano [10] drew attention to the fact that, derived from the uncertainty relation, an energylossf15 eV from a high-speed (fc) particle cannot be localized within f90 nm Thatsuch energy losses in a condensed medium would give rise to collective excitations(plasmons) was a source of some concern until recently On the other hand, understanding

of radiation-induced transformations, operation of detectors, etc would require that thedeposited energy be localized in a molecule before dissociation or ionization can occur.Because no reasonable explanation has yet been proposed for the localization of energyafter the initial delocalization, rationalization has been advanced as the delocalizationapplying only to the first interaction [4] After that, all energy losses are localized andcorrelated on a track [11]

Nevertheless, certain collective excitations can occur in the condensed phase Thesemay be brought about by longitudinal coulombic interaction (plasmons in thin films) or bytransverse interaction, as in the 7-eV excitation in condensed benzene, which is believed to

be an exciton [12] Special conditions must be satisfied by the real and imaginary parts ofthe dielectric function of the condensed phase for collective excitations to occur Afteranalyzing these factors, it has been concluded that in most ordinary liquids such as water,collective excitations would not result by interaction of fast charged particles [13,14]

2 STOPPING POWER, LET, AND FLUCTUATIONS

2.1 Bohr’s Theory and the Bragg Rule

The rate of energy loss of a charged particle per unit pathlength is called the linear energytransfer(LET) The corresponding energy received by the medium, which remains in thevicinity of the particle track, is designated as the stopping power Therefore LET andstopping power refer to the penetrating particle and the medium, respectively The dif-ference between these quantities arises because, even in the shortest time scale (f1015s),some of the deposited energy may be removed from the track vicinity by fast secondaryelectrons, by Cerenkov radiation, and, in the case of ultrarelativstic particles, by bremss-tralung Cerenkov radiation is seen as a faint bluish light when the speed of the penetratingparticle (usually an electron) exceeds the group velocity of light in the medium Although

it contributes negligibly to the LET, it has importance as a time marker, because it isemitted almost instantaneously The term LET was first coined by Zirkle et al [15] in aradiobiological context, replacing some earlier nebulous terminology Both LET andstopping power are average concepts and considerable fluctuations are to be expectedaround these values The physical theories of energy loss rate should refer to LET, butthese are often called stopping power theories The International Commission on Ra-diation Units and Measurements recommends the use of the symbol LAto denote energytransfers below a limit A Thus L100would denote LET for energy losses of less than 100

eV and Llwould include all energy losses

The first successful theory of stopping power is attributed to Bohr [16,17] He takesthe simplest case of a fast, yet nonrelativistic, heavy particle of velocity v and charge ze,where e is the electronic charge Under this condition, the basic electrostatic interactioncan be treated as a perturbation, that is, the particle path can be considered to be virtuallyundeflected In addition, the energy losses occur through quasi-continuous inelastic col-lisions with medium electrons, so that the average stopping power is a good representation

of the statistical process of energy loss All stopping power theories recognize these

sim-plifications Neglecting the binding energy of the electron and calling the distance ofclosest approach of the incident particle as the impact parameter b, it may be shown thatthe component of momentum transfer parallel to the particle trajectory vanishes bysymmetry and that, perpendicular to the trajectory, is given by 2ze2

/bv [18] The sameexpression is obtained by multiplying the peak forceze2

/b2with the so-defined duration

of collision2b/v Thus the energy transfer is given by Q = (2ze2

/bv)2/2m = 2z2e4/mb2v2,where m is the electron mass The differential cross-section for this process is given geo-metrically as:

dr¼ pdðb2Þ ¼ ð2pz2e4=mv2ÞðdQ=Q2Þ;

which is just the Rutherford cross-section for scattering by free charges receiving theenergy transfer Q For application to bound electrons which can be excited (or ionized),for the same momentum transfer, to the nth state with energy En, Bohr surmised the sumrule AnfnEn¼ ZQ, where Z is the atomic number and fnis the oscillator strength of thattransition (see later for proper definition) The stopping power dE/dx is the energy loss

to all the medium electrons per unit path of the incident particle, over all permissibleenergy transfers Therefore

dE=dx ¼ NZ

drX

n

fnEn¼ ð2pz2e4NZ=mv2ÞlnðQmax=QminÞ: ð1ÞFor the maximum energy transfer, binding effect may be ignored, giving in the non-relativistic case Qmax = 2mv2 For the minimum energy transfer, Bohr argued that col-lisions must be sudden so that an effective energy loss may occur That is, the collision time2b/v must be Vt/E1, where E1 is atypical atomic transition energy and t is Planck’sconstant divided by 2p This gives bmax=tv/2E1and Qmin= 8z2e4E1/[(mv2)(t2

v2)] stituting in Eq (1), one obtains

where the expression within the parentheses in Eq (2) is called the kinematic factor and B,denoted as the stopping number, is given in Bohr’s theory as Z ln[(2mv2/E1)(tv/4ze2

)].Although the impact parameter is not an observable quantity, Bohr’s theory has a widerange of validity if the typical transition energy E1is properly chosen Equation (2) alsoshows the typical structure of a stopping power equation as a product of a kinematicfactor and a stopping number The kinematic factor is free from any target property,which is solely contained in the stopping number In most stopping power expressions, thekinematic factor therefore remains the same as in Eq (2)

As it stands, Bohr’s theory is only applicable to atoms To extend it to molecules andmixtures, one invokes the Bragg rule, originally used for charged particle ranges in ion-ization chambers Simply stated, the Bragg rule equates the stopping number of the mol-ecule (or the mixture) to the weighted sum of the stopping numbers of the constitutingatoms Bragg’s additivity rule applies impressively within a few percent for many com-pounds However, the contribution of an atomic stopping number in different compounds

is not necessarily the same as that for the free atom That this contribution remains thesame in each case indicates the similarity of that atomic participation in various com-pounds The apparent success of Bragg’s rule has been traced to two factors: (1) similarity

of atomic binding in different molecules, and (2) electronic transitions that have the mostoscillator strengths involve excitation energies far in excess of chemical binding Wheresuch is not the case as, for example, in H2, NO and compounds of the lightest elements, therule does not hold well There is evidence that the Bragg rule starts to break down at lowincident energies The quantum mechanical theories of stopping power are also amenable

to this additivity rule in a similar fashion (see Sec 2.2) However, this does not mean thatthe ensuing chemical response of the molecule is necessarily related to those of the con-stituent atoms There are definite effects of chemical binding and state of aggregationwhich alter the energy levels and the oscillator strengths of transitions The Bragg rulerefers only to the stopping of the incident particle.

2.2 Bethe’s Theory and Extensions

The first (and still the foremost) quantum theory of stopping, attributed to Bethe [19,20],considers the observables energy and momentum transfers as fundamental in the inter-action of fast charged particles with atomic electrons Taking the simplest case of a heavy,fast, yet nonrelativistic incident projectile, the excitation cross-section is developed in thefirst Born approximation; that is, the incident particle is represented as a plane wave andthe scattered particle as a slightly perturbed wave Representing the Coulombic interaction

as a Fourier integral over momentum transfer, Bethe derives the differential Born section for excitation to the nth quantum state of the atom as follows

In Eq (3), q is the magnitude of the momentum transfer, Q = q2/2m is the energy of

a free electron having that momentum q, and other kinematic parameters have the samesignificance as in the Bohr theory The quantity, FnðqÞ ¼ Sjn

expð2pihq  rjÞ

0

, called theinelastic form factor, is the sum over all the target electron coordinates, of the matrixelements of the exponential operator involving the vector momentum transfer q betweenthe ground and the nth excited state Obviously, the stopping power would be obtainedfrom Eq (3) asdE=dx ¼ N SnmQmax

QminEndrn, where N is the atomic number density, Enisthe transition energy, and Qminand Qmaxstand for the minimum and maximum values of

Q, respectively, consistent with a given excitation energy It is convenient to divide therange of Q into small and large momentum transfers [3] In collisions involving smallmomentum transfers, sometimes called soft or glancing collisions, Bethe shows that

jFn( q)j2!Qfn/En, where fn is the corresponding dipole (optical) oscillator strength (videinfra) This allows the contribution of such collisions to the stopping power to be written(cf Eq (3)) as ð2pz2e4N=mv2Þ Snfn ln Q1

ðE 2 =2mv 2 Þ, where Q1 is the rather inconsequentialupper limit of Q for small momentum transfers, and Qmin, for excitation energy En, isgiven kinematically as En2/ 2mv2 For large momentum transfer collisions, sometimes de-signated as hard or knock-on collisions, Bethe directly proves the sum ruleSnEnjFðqÞnj2

¼ ZQ Inserted into Eq (3), one then obtains the contribution of hard collisions to thestopping power as (2pz2e4N/mv2)Z ln(2mv2/Q1), where Q1is taken as the lower limit of Qfor hard collisions and the kinematic maximum 2mv2 is used for Qmax Noting theThomas–Kuhn sum rule Snfn¼ Z, the total number of electrons in the atom, and addingthe contributions of soft and hard collisions, the total stopping power is then given by

theory gives a meaning to the mean excitation potential I in terms of strengths and gies of atomic transitions and underscores the importance of the dipole oscillator strength.

ener-It should be noted that, in the definition of the mean excitation potential [Eq (5)], as well

as in the derivation of the Thomas–Kuhn sum rule, excitation to energetically inaccessiblestates are also formally included At a sufficiently high incident velocity for the Born ap-proximation to be valid, it usually does not entail much error However, it is a separateapproximation Another approximation, called Bethe’s asymptotic cross-section, derivesfrom expanding the interaction cross-section at high incident energies and retaining onlythe lead term [21] A simplified derivation of Bethe’s formula has been given by Magee[22]

Several extensions of the basic stopping power theory of Bethe can be made Forcompounds and mixtures, Bragg’s additivity rule may be applied with the resultant value

of I given by the geometrical average of the mean excitation potentials of the constituentatoms over their electron numbers In the case of incident electrons, Qmax, ignoring atomicbinding, would be given by (1/4)mv2rather than by 2mv2, because the distinction betweenthe incident and the secondary electron can only be made on the basis of energy.Incorporating this modification, Bethe gives BðelectronÞ ¼ Z lnðmv2=2pffiffiffiffiffiffiffiffiffie=2IÞ, where e

is the base of natural logarithm Thus the electron stopping power at the same velocity isalways a little less than that of a heavy particle, sometimes by as much as 20%

At relativistic speeds, the maximum energy transfer increases to 2mv2/(1b2

), where

b = v/c Also, electromagnetic effects have to be considered in addition to electrostaticinteraction These result in the addition of a term Z [ b2+ln(1b2

)] to the stoppingnumber This extra stopping, called the relativistic rise, is proportional to b4for smallvalues of b Its effect is <0.1% for v<5
109cm sec1, but it can be very significant whenvfc Fermi showed that the electronic stopping power would diverge were it not for themutual polarization screening of medium electrons This effect, therefore, is moreimportant in the condensed phase and is called a density correction This correctivefactor, added to the stopping number, is denoted byZd/2, where d = ln[ tx2

p/I2(1b2)]1and xp= (4kNe2

Z/m)1/2, denoted as the plasma frequency [3] Another correction is ally needed when the incident particle is not faster than the speed of atomic electrons, asrequired for the validity of the Born approximation This is more important for the Kelectrons, but it is also sometimes needed for the L electrons in heavy elements Denotingthe total so-defined shell correction as C, the result is a little reduction of the stoppingnumber by that amount Combining the effects of relativity, density, and shell corrections,the Bethe stopping number of a heavy particle is given by

usu-B¼ Zðln 2mv2=I  b2 lnð1  b2Þ  C=Z  d=2Þ: ð6ÞThe corresponding stopping number for the electron is given by

BðelectronÞ ¼ ðZ=2Þ



ln mc2b2E=2I2ðI  b2Þ 

2

Slow positive ions tend to capture electrons from the medium when their speeds fallbelow z1v0, where z1 is the bare nuclear charge and v0 is Bohr’s velocity At first, the

captured electron is promptly lost in a subsequent charge-changing collision The cycle ofcapture and loss continues for a while and an equilibrium charge is established Theincident charge in the stopping number should then be changed from z to zeff, given by

hz2i1/2

, where the angular brackets indicate averaging with respect to charge-changingcollision cross-sections After the first electron is firmly captured, another cycle of electroncapture and loss may continue until a second electron is firmly captured, and so on Thenet effect of charge changing collisions is to lessen the stopping power a little because zeffisalways <z Even so, electron capture and loss constitute minor energy loss processes bythemselves

Despite the apparent similarity of the Bohr and the Bethe stopping power formulae,the conditions of their validity are rather complimentary than the same Bloch [23] pointedout that Born approximation requires the incident particle velocity v>>ze2/h, the speed of

a 1s electron around the incident electron while the requirement of Bohr’s classical theory

is exactly the opposite For heavy, slow particles, for example, fission fragments ing light media, Bohr’s formula has an inherent advantage, although the typical transitionenergy has to be taken as an adjustable parameter

penetrat-2.3 Dipole and Generalized Oscillator Strengths: Sum Rules

From the inelastic form factor (see Sec 2.2), Bethe [19] defines a generalized oscillatorstrength fn( q)u EnFn( q)2/Q, for excitation with an energy loss En, simultaneously with amomentum transfer q, in close association with the (optical) dipole oscillator strength Thelatter may be obtained experimentally from the absorption coefficient a(v), viz fn= (mc/

pnVc2

)ma(v)dv, where nV is the medium refractive index and the integration is carried overthe frequency v for the same transition Theoretically, it is related to the dipole momentmatrix element for the transition from the ground to the nth state through the EinsteinA—coefficient as fn¼ ð8pmv=e2hÞgnhnje Sjxjj0i2

Here gnis the degeneracy of the excitedstate (the ground state is taken as nondegenerate), xjis the x component of the position ofthe jth electron, and the summation is carried over all the atomic electrons Expanding theexponential in the inelastic form factor [see Eq (3) et seq.] for a small momentum transfer,and noting the orthogonality of the wave functions, one obtains limq !0fnðqÞ ¼ fn, thusestablishing a relationship between the generalized and dipole oscillator strengths.Fig 1shows such a procedure for the electron impact excitation in helium at an incident energy

of 500 eV [24] Platzman [25] advocated the construction of a complete optical spectrum( fn), and therefrom, that of the excitation spectrum ( fn/En) [cf Eq (3) and the definition ofthe generalized oscillator strength], from a few experimental determinations augmented bythe various sum rules However, the results in the cases of methane and water were notvery satisfactory, probably because of the unavailability of a sufficient number of dipolesums of adequate accuracy

Both generalized and dipole oscillator strengths satisfy sum rules, which can be used

to unravel their character, although their calculation from first principles is not easy exceptfor the lightest elements For the dipole oscillator strength, a sum may be defined bySðlÞ ¼X

n

where the sum is over all the states of excitation, including integration over continuumstates (here and in later discussion) S(0) = Z, the number of electrons in the atom ormolecule This is called the Thomas–Kuhn sum rule Bethe [19] has shown that the samerule is satisfied by the generalized oscillator strength for any momentum transfer,

i.e.,SnElnFnðqÞ ¼ Z, for any q Considering the oscillator strength as a normalized bution, S(l) in Eq (8) may be taken as the lth moment of the transition energy WhileS(l) diverges for lz 3 in systems where the ground state electron density is nonvanishing

distri-at the nucleus [21], for 4 V l V 2, the sums are related to important physical properties[26] S(4) may be experimentally obtained from the refractive index and the Verdetconstant, the latter referring to the rotation of the plane of polarization per unit thicknessper unit magnetic field parallel to the propagation direction S(2) = a/4, where a is thepolarizability S(2) = (16pZ/3)times the average electron concentration at system center.S(1) is related, apart from a constant ground state energy, to momentum correlation ofelectrons [26] S(1) equals the total dipole matrix element squared, M2

tot¼ Si ; j xixj

,which appears as a lead term in the total inelastic collision cross-section [27]

Another class of sum rules may be defined as logarithmic moments, or by formallydifferentiating S(l) with respect to l [see Eq (8)], yielding

et al [24], with 500-eV incident electrons The abscissa is the square of the momentum transfer

the optical oscillator strength, is attained irrespective of the validity of the Born approximation

incident energy

quantity [27] Oscillator strength sum rules have been used with success, limited chiefly tothe lightest atoms, in amending uncertain oscillator strengths and in calculating a range ofphysical properties including the refractive index and the Verdet constant [26] Thus, forexample, the dipole oscillator strength of the transition 21Pp11Sin helium was corrected

by Miller and Platzman [28] to 0.277, against an earlier calculated value of 0.19

2.4 Special Features of the Condensed Phase

One aspect of the condensed phase regarding the delocalization of the deposited energyhas been alluded to in Sec 1.3 Here we will consider the modifications on the oscillatorstrength and the mean excitation potential, due to condensation, which would enter inBethe’s stopping power theory [see Eqs (4–7)]

For polyatomic molecules such as water, the oscillator strength is, in general,continuously distributed because of any combination of dissociation, ionization, etc.The stopping power is then determined by the differential oscillator strength distribution(DOSD) Phase effects occur naturally through the DOSD In the gas phase, lightabsorption and/or inelastic scattering experiments can be used to obtain the DOSD,and a fairly complete determination has been made for water vapor [29] In the condensedphase (solid or liquid), absorption measurement in the far-UV and beyond is experimen-tally very difficult In such cases, an indirect method, depending on electromagneticrelationships, can be sometimes used if reflectance measurements are available at thevacuum–liquid (or vacuum–solid) interface over a wide range of energies Denoting thereflectance at energy E as R(E), the phase angle is obtained from the Kramers–Kronigrelation, /ðEÞ ¼ ðE=pÞPml

0 ln RðEVÞdEVðEV2 E2Þ1, where P is Cauchy’s principal valuefor the integral From these, the real and imaginary parts of the refractive index areobtained as n = (1R)/(1+R2R1/2cos /) and k = (2R1/2sin /)/(1R2R1/2

cos /),respectively The real and imaginary parts of the dielectric function are then given by

There is an upper limit of experimental reflectance measurement, usually around 26

eV With present-day synchrotron sources, this limit is being progressively extended.Nevertheless, in the global integration of the Kramers–Kronig relation, a long extrap-olation is needed In the original experiments of Heller et al [30] on liquid water, anexponential and a power-law extrapolation beyond the upper limit of experiments wereused Later, LaVerne and Mozumder [31], requiring transparency in the visible region andthe correct number of valence electrons (8.2 for water), opted for the power-law with index3.8, close to the theoretical limit of 4.0 for valence electrons The contribution of the Kelectrons remains the same as in the gas phase and are, therefore, simply added The so-determined DOSD for liquid water is shown inFig 2,and compared with that of the gasphase given by Zeiss et al [29], and with that of gaseous cyclohexane, obtained byKoizumi et al [32] by using synchrotron UV-absorption measurement In water, there aretwo main effects of condensation First, there is a loss of structure in the condensed phase.Second, there is an upward shift of the excitation energy The peak in the DOSD changesfromf18 eV in the gas phase to f21 eV in the liquid phase This means that collisions inthe liquid phase are more difficult Using the oscillator distribution, the computed values

of I, the mean excitation potential is 74.9 and 71.4 eV for liquid and gaseous water,

respectively [31] This difference may not seem critical in determining the stopping power.However, the nature and energy of the excited states are different in the two phases,yielding different chemical outcomes (see later).

2.5 Range–Energy Relation

The range of an incident particle is defined as the average crooked path length between theinitial and final energies, while penetration refers to the vector distance between thestarting and ending points The difference between these quantities is attributed toscattering, mostly elastic Obviously, range increases with initial energy The range–energyrelation is important for the identification and energy measurement of charged particles, atool that is routinely used in nuclear physics In radiation chemistry, it provides a basis forcharged particle tracks and the reactions on them Various tables of ranges of light andheavy particles are now available, of which an earlier collection [33] and a latercompilation by Ziegler [34] are noteworthy

Range, obtained by (numerical) integration of the stopping power as, R¼mEi

E0dE=ðdE=dxÞ, is called the continuous slowing down approximation (CSDA) range Here Ei

is the initial energy, E0is the energy where the particle is considered stopped, and theapproximation refers to the stopping power being a continuous function of energy,ignoring random fluctuations For electronic stopping, E0 should be the energy of thefirst excited state, but a higher value is often adopted for fast incident particles, because, at

curve, B] and in gaseous cyclohexane [32, curve, C] Data in liquid water are obtained from ananalysis of UV-reflectance and that in cyclohexane, from synchrotron–UV absorption The Thomas–Kuhn sum rule is satisfied approximately in each case

low energies, the stopping power formula is not reliable and, in any case, it is superseded

by subelectronic processes Such an arbitrary value of E0becomes inconsequential if theincident energy is sufficiently high

Often, the range–energy relation is displayed as a power law, R~Em

, where the index

mwould approach 2 if the slow variation of the stopping number B with particle velocity isignored [see Eq (4) et seq.] For protons and He ions of a few hundred MeV, mapproaches 1.8, decreasing somewhat with decreasing energy The index m also depends

on the medium traversed For electrons in water, it diminishes gradually from f1.7 tof0.9 as the initial energy is decreased from a few thousand to a few hundred eV Low-energy electron range in water is of great importance to the spur theory of radiationchemistry, but it is also rather difficult to ascertain and often greatly influenced by elasticscattering This field is being continually improved and track simulation techniques havebeen employed [35], which give not only the mean range, but also its distribution (see thenext section) However, very little is known about elastic scattering in liquid water, forcingmany investigators to use gas phase data for that purpose Typical values of computedranges in water are f550 nm for 5-keV electrons, f0.5 mm for 5-MeV protons, andf0.04 mm for 5-MeV a-particles Ranges of slow heavy ions and fission fragments arenearly proportional to energy, because the increase of stopping power in relation toslowing down is largely compensated by a lowering of effective charge as a result ofelectron capture, thus providing an almost constant stopping power The typical density-normalized range of Ne ions of 10 MeV/amu in Al is 40 mg/cm2

2.6 Discussion of Stopping Power, Range, and Fluctuations

The most important factor in Bethe’s stopping power equation, which embodies theaggregate effect of transition energies and oscillator strengths, is the mean excitationpotential, I [see Eqs (4) and (5)] Its direct calculation requires the knowledge of theground and all excited state wave functions Such a calculation for atomic hydrogen gives

I= 15 eV, whereas in atomic binding in different molecules, a value of 18 eV is preferred

to satisfy the Bragg rule [3] For other atoms, application of the Thomas–Fermi model byBloch shows that the spectral distribution of the oscillator strength has universal shape inall atoms, if the transition energy is scaled by Z This means I~Z, with the constant ofproportionality beingf12 eV A detailed examination of the Thomas–Fermi–Dirac modelgives I/Z = a+bZ2/3, with a = 9.2 and b = 4.5 as best adjusted values, and where I isexpressed in eV This equation agrees rather well with range experiments However, Fano[3] points out that it should not be construed as a validation of the statistical model of theatom I, being a logarithmically averaged quantity, can be well approximated without anaccurate knowledge of the distribution An error yI in determining I only appears as arelative error off(1/5)yI/I in the evaluation of range In practice, I is often treated as anadjustable parameter to be fixed by range measurement of fast protons or a-particles Withknown I values of constituent atoms, the mean excitation potential of a molecule may beobtained by the application of the Bragg rule (see Sec 2.1) Thus if the molecule has nIatoms of atomic number ZI, and mean excitation potential II, then the overall meanexcitation potential of the molecule would be given by the relation Z ln I =SniZiln Ii,where Z =SniZiis the total number of electrons in the molecule

The stopping power of water, over a wide span of energy, for various incidentparticles has been discussed elsewhere [Ref [4], Sec 6], with special consideration foreffects at low and very high energies Generally speaking, the electronic stopping powershows a peak at a relatively low energy (f100 eV for incident electrons and f1 MeV forincident protons), as a result of the combined effect of the velocity denominator in the

kinematic factor and the logarithmic velocity dependence in the stopping number [c.f., Eq.(4) et seq.].

The usual stopping power formula for low-energy electrons (Born–Bethe imation) requires corrections on two accounts First, the integrals defining the totaloscillator strength and the mean excitation potential must be truncated at the maximumenergy transfer (c(1/4)mv2), resulting in the replacement of Z and I by Zeff and Ieff,respectively[36] These quantities are lower than their respective asymptotic values andtheir effects partially cancel each other Second, the effect of the nonvanishing of themomentum transfer for inelastic collisions becomes significant When a quadratic exten-sion of the generalized oscillator strength is made in the energy-momentum plane stillusing the DOSD, the net effect is expressible as a reduction of the electron stoppingnumber by an amount Zeff(e/2E)ln(4e˜E/I ), where e˜ is the base of natural logarithm, E isincident electron energy, e is average energy loss in an encounter, and I is a mean energydefined by Zeffe ln I ¼m

approx-0

e max

e ln efðeÞde [36] Here emaxis the maximum transferable

ener-gy In track simulation procedure, it is more convenient to work with basic cross-sections(with which the stopping power is calculated) and keep a detailed account of energy loss,distance traversed, etc The stopping power may then be computed from definition byaveraging over a large number (typically f104

) of simulations The results of such acalculation by Pimblott et al [35] is shown inFig 3 for water in the gaseous and liquidphases The difference, of course, is directly traceable to that in the DOSD as discussedearlier

Even if the statistical fluctuation of energy loss is ignored, there would be a differencebetween the CSDA range and the penetration, because of large-angle elastic scattering (seeSec 2.5) The distribution of the final position vector of the penetrating particle can beobtained in terms of its energy-dependent stopping power and the differential cross-section

of scattering [36] Actual calculation in the general case is complex, but it simplifies siderably when the number of scatterings are >>1 The distribution can then be shown asgaussian and spheroidal, i.e., W(r) = (2pA)1(2pB)1/2exp[{(x2

con-+y2)/2A+(zhzi)2

/2B}],where A =hx2i and B = hz2ihzi2

, and the angular brackets refer to mean values Themean square radial penetration is then given by r 2

¼ 2pml

0 r4drmp

0WðrÞsin hdh, where h isthe angle of the position vector relative to the z-axis, the initial direction of motion Theroot mean square (rms) range, defined by hr2i1/2

is often the more significant quantity.Fig 4shows the CDSA and rms ranges in gaseous water as functions of electron energyaccording to LaVerne and Mozumder [36] In these calculations, stopping power was com-puted by the procedure detailed above The scattering cross-section was fitted to swarmand beam data by adopting Moliere’s modification of screened Rutherford scattering It isobvious that the rms range is always shorter than the CSDA range, the difference becomingmore significant at lower energies The following general observations can be made for thepenetration distribution (1) The memory of the initial direction is maintained by theelectron until it has lostf80% of the starting energy, after which the distribution becomesspherical (2) The electron penetrates a certain distance with only a few scatterings and thendiffusive motion sets in (3) The number of elastic scatterings needed to give a sphericaldistribution increases with energy, beingf15 and f74, respectively, for electrons of 1 and

10 keV energy in water

Because of the statistical nature of collision processes, charged particles starting withthe same energy do not travel the same distance after losing a fixed amount of energy, nor

do they have the same energy after traveling a fixed distance, respectively giving rise topathlength stragglingand energy straggling Fano [3] adds a third kind of distribution ofdistance for particles that have dropped below a certain energy at the last collision, which

is not necessarily the same as pathlength straggling, because of the discrete nature of theenergy loss process While all these distributions are related, the most importantdistribution is range straggling when the final energy is reduced to insignificance Bohr[17] considers a group of energy losses and a large number of loss processes in each group,thereby obtaining a gaussian distribution by virtue of the central limit theorem Thismeans (d/dx)hDE2i = 4pe4

z2NZ, wherehDE2i is the mean square fluctuation in energy loss

of particles after traversing a distance x The corresponding pathlength and rangedistributions are also gaussian These considerations apply mainly to heavy particles ofrelatively high energy penetrating virgin media The ratio of the root mean square rangedispersion to the mean range is typically a few percent for a heavy particle, but may be afew tens of percent for electrons of moderate energy Straggling is always more importantfor electrons of any energy because of the large fractional energy that an electron can lose

in a single encounter Also, if the sample penetrated is thin, the resultant energy

function of electron energy according to track simulation by Pimblott et al [35] There is a noticeable

distribution of emergent particles of any kind will not be gaussian, but will show a highenergy tail Such Landau–Vavilov distribution has been extensively tabulated [33], havingexperimental justification Its application to radiation biology derives from the fact thatthe radiation effect in a cell depends on the energy deposited in it, while the cell size is oftensmall compared to the particle range [37].

A collision-by-collision approach was introduced by Mozumder and LaVerne [38]for range straggling of low-energy electrons without the consideration of large-angleelastic scattering The probability density of pathlength x for the first collision is given by

P1(x) = K1 exp(x/K), where the mean free path K is computed from the same ential cross-section of energy loss as used in the stopping power (vide supra) The integral

differ-of the energy-loss weighted differential cross-section hei gives the mean energy loss in asingle inelastic encounter The ratio, hei/K, gives the spatial rate of energy loss for thatencounter, while the true stopping power is the mean value of the ratio of energy loss topath length To this extent, the procedure is an approximation To have a pathlengthdistribution Pn(x) in n collisions, the electron must have had a distribution Pn1(xy) in(n1) collisions and a distribution P1( y) in the last collision This generates a convolution,

j ¼1ð1  Kj=KiÞ1ð j p 1Þ Note that the mean free paths are energy-dependent Therefore

a concurrent use of the stopping power is required to give the electron energy after eachcollision To obtain the range distribution, the total number of collisions is so adjustedthat the mean final energy becomes immaterial Thus, as shown inFig 5,Mozumder andLaVerne [38] give the range distribution of 200-eV electrons in N2 by convoluting thepathlength distributions between energies 200 to 110 eV and between energies 110 to 31

eV In this case, the final energy has been taken to be twice the ionization potential Notice

gaseous water according to LaVerne and Mozumder [36] See text for details

that, in these calculations, the fundamental input still remains to be the DOSD Thefollowing remarks may be made about the range distribution of low-energy electrons (1)For electron energies below about 5 keV, CSDA>mean>median range CSDA range isthe least reliable because it considers energy losses in a continuous manner within themean free path (2) At low energies, the distribution is skewed toward longer ranges Theskewness parameter approaches the gaussian limit of unity above f10 keV, almostindependent of the material traversed (3) The most probable density-normalized rangefor a 1-keV electron in H2O, N2and O2is 6.1, 7.1, and 8.4Ag/cm2

, respectively However,relative straggling, given by the ratio of FWHM of the range distribution to the mostprobable value, is nearly independent of the medium, being 1.4, 0.7, and 0.4 at energies of

100, 500, and 2000 eV, respectively

So far, the discussion presented here is based either on penetration deriving fromlarge angle elastic scattering, or on the statistical nature of inelastic collisions givingstraggling As yet, there has not been any analytic theory that combines both, but MonteCarlo simulation, including some form of realistic differential cross-section of elasticscattering, shows promise [35]

3 SECONDARY IONIZATION

3.1 Cross-Sections

Ionizations produced by electrons generated in the primary interaction of the incident fastcharged particle are called secondary The definition may be extended to all successivegenerations if sufficient energy is available In this sense, secondary ionization is very

at 110 eV [38] The final energy is about twice the ionization potential See text for details

important and it is a ubiquitous feature of all fast primary charged particles Typically,f25% of all ionizations are produced in secondary processes Of course, experimentscount all ionizations, irrespective of whether they are primary or secondary.

The importance of total ionization yield derives from dosimetry and from providing

a standard against which other radiation–chemical yields may be discussed [25] For thecomplete description of impact ionization, a fivefold differential cross-section is required inprinciple; one for ejected electron energy and two each for the angular distributions of theejected electron and the incident particle Such a detailed description is rarely needed Inradiation chemical track structure, a cross-section doubly differential in the energy andangle of the ejected electron is sufficient Moreover, the Born approximation, againstwhich measurements and numerical calculations may be compared, starts to break down

as the incident energy is decreased The onset for this breakdown occurs at a greaterenergy if higher order differential cross-sections are considered A special issue ofRadiation Research [39] contains articles written by several experts on the experimentaland theoretical aspects of impact ionization, including higher order differential cross-sections The calculation of the impact ionization cross-section for incident velocity vproceeds, in the Born–Bethe approximation, in the same manner as that for energy loss(see Sec 2.2) In effect, energy loss is written as Wi= E+II, where E is the secondaryelectron energy and IIis the ionization potential for the ith orbital from which the electron

is ejected Combining the contribution from all the orbitals in the atom or molecule, thedifferential ionization cross-section for ionization may be given as follows [40]

dE )(T/4pa02z2)(W/R)2, and its plot vs R/W is called the Platzman plot [see Eq (19) et seq

of Chap 3] Here W = E+B1 and B1 is the lowest binding energy of the electron inthe molecular orbital The usefulness of such a plot rests on: (1) limW!l¼ Z, the totalnumber of electrons, (2) autoionization and Auger processes show up as dips or peaks, (3)for small values of E, Y resembles the shape of W(df/dW), and (4) in proton impact, apeak is seen at ejected electron speed equal to the speed of the proton Furthermore, thearea under the Platzman plot is proportional to the total ionization cross-section, theconstant of proportionality being T/4pa0R Kim [40] has made repeated use of the Platz-man plot in a careful analysis of secondary electron spectra, in some cases correcting someexperimental values Another plot, (T/R)(dr/dE) vs ln(T/R), called the Fano plot, isuseful in extrapolation and interpolation of experimental data It approaches a straightline at high T

The above considerations need relativistic correction at vfc, which may beperformed in a straightforward manner More importantly, Eq (10) assumes that theionization process is direct, i.e., once a state above the ionization potential is reached,ionization occurs with a certainty Platzman [25] points out that in molecules, this is notnecessarily so and superexcited states with energy exceeding the ionization potential mayexist, which will dissociate into neutral fragments with a certain probability For example,

in water in the gas phase, ionization occurs with a sharp threshold at the ionizationpotential (I.P.)=12.6 eV, but only with an efficiency of 0.4 Beyond the I.P., the ionization

efficiency, determined by the ratio of ionization to the photoabsorption cross-section, varieswith the energy untilf18 eV, beyond which it approaches unity [41] In such cases, thecross-section formula given in Eq (10) must be suitably modified to account for theionization efficiency There is a very definite phase effect on the ionization efficiency,because of which the existence of superexcited states in liquid water has recently beenquestioned [42] The typical values of proton impact ionization cross-section in the gasphase, for H, He,H2, N2, CO2, NH3, and CH4are 1.12, 0.93, 1.96, 5.33, 8.11, 4.62 and 6.84

A2, respectively, at 100 keV, and 0.19, 0.21, 0.38, 1.46, 2.13, 1.30, and 1.66, respectively, at 1MeV Rudd etal [43] have given an empirical formula for the total ionization cross-sectiondue to a heavy ion at energy U, viz rt 1= r1 l +rh 1, where rh(A2) = 3.52(R/U)(A ln[1+U/R]+B) and rt(A2) = 3.52C(U/R)D This form has the correct asymptotic behavior given bythe Born–Bethe cross-section at high energy The parameters A, B, C, and D have beentabulated, and a similar formula for incident electrons is also available The correspondingsecondary electron spectrum involving some 10 adjustable parameters has been empiricallyfound to be very useful It is discussed in some detail in Chap 3 [Eqs (29)–(35)]

3.2 The Degradation Spectrum

The complexity of electrons of different energy and generation actually present in anirradiated system, together with their primary counterparts, if different from the electron,

is represented by the degradation spectrum, which is defined to be the normalized energyspectrum of these particles flowing through the surface of a small cavity inside themedium Spencer and Fano [44] show that a convenient measure of this spectrum is given

by y(T0,T ), such that y(T )dT is the total mean distance traveled by electrons of allgenerations (primary, secondary, etc.) between energies T and T+dT, with T0being theinitial energy at unit flux The degradation spectrum serves a purpose similar to thedistribution function in statistical mechanics, in the sense that the yield of any primaryspecies x is given by NxðT0Þ ¼ NmT 0

IxrxðTÞyðT0; TÞdT, where rxis the cross-section for theproduction of x with an energetic threshold Ix(e.g., for ionization) Note that y needs to beevaluated only once for each initial energy, after which it may be used for all products.Although y depends on T0, some approximate scaling property of the electron degradationspectrum has been noted [45]

Calculation of the degradation spectrum has proved to be difficult in all but thesimplest cases of H, He, and H2, because of the lack of accurate energy-loss cross-sections(mainly nonionizing) over a wide span of energy Furthermore, to calculate the yield of aparticular species, its own production cross-section must be known over a wide interval ofenergy, which is rarely available In the continuous slowing down approximation (CSDA),the contribution to the degradation spectrum of a single electron is the reciprocal of thestopping power Therefore after knowing the ionization cross-section and the electronstopping power, one can compute the partial degradation spectrum generation bygeneration Finally, the total degradation spectrum may be obtained by summing up.Such a procedure has been followed by Kowari and Sato [46] for gaseous water Apartfrom demonstrating the methodology, the actual results are of limited use because ofvarious dubious cross-sections used More sophisticated methods employ the Spencer–Fano equation [45], or the Fowler equation [47]; however, the problem of accurate cross-sections still remain in most cases Another numerical approach by Turner et al [48] relies

on Monte Carlo simulation Their computed spectra show considerable difference betweenthe gas and liquid phases of water, especially in the low energy region, which is a directconsequence of the peculiar kinds of cross-sections used by them in these phases Onefeature is common to all electron degradation spectra It has large values at the high

starting energy and also at very low energies The former is attributed to low stoppingpower and the latter is attributed to the accumulation of electrons of different generations.Therefore the spectrum is expected to show a drop at some intermediate energy, often nearwhere the stopping power goes through a broad peak It should be noted that, like thestopping power and the range, the degradation spectrum also refers to mean values, andconsiderable fluctuation may be expected, especially at higher energies.

3.3 The W Value

The reciprocal of the ratio of the mean number of ionizations niproduced by the completeabsorption of a primary particle of energy T is defined as the (integral) W value Ioniza-tions produced by all secondary electrons are counted in it A differential, or track segment

x value, may be similarly defined, so that 1/x = (d/dT )(T/W ) If W is independent of T,

so is x and vice versa Generally, W depends weakly on T, unless the initial energy is verylow Its dependence on the nature of the incident radiation (electrons, alpha-particles, etc.)

is also minor These factors constitute the basis of dosimetry, by collecting and measuringthe total ionization It also means that the Bragg curve, or the variation of total ionizationwith incident particle energy, is a reliable measure of the relative stopping power Thus the

Wvalue is mainly a property of the medium, determined by the cross-sections of tion and of other nonionizing energy-loss processes As such, the W value often depends

ioniza-on the phase

Platzman’s [49] analysis for the W value may given as W =hEioni+vexhEexi+hEsi,where hEioni, hEexi, and hEsi are the average energies for ionization, excitation, andsubexcitation electrons, respectively, and vex is the relative number of excitations toionizations It provides a basis for understanding the insensitivity of W on particle energy,because the quantities involved depend not so much on absolute cross-sections forionization and nonionizing energy loss, as it depends on their ratio

An early theory of the W value was proffered by Spencer and Fano [44], based on thedegradation spectrum Another method, the Fowler equation, was employed by Inokuti[47] for electron irradiation, based on the approximation that there is only one ionizationpotential and that the ionization efficiency is unity These restrictions can be relaxed Themain result of Inokuti’s analysis may be given as follows

In Eq (11), Wlis the asymptotic W value at very high energy, I is the ionization potential,

Uis a so-defined energy parameter, and EV is interpreted as the average energy transfer

in ionizing collisions where the ejected electron is subionization, i.e., incapable of furtherionization Thus, U is the excess of EV over the ionization potential An expression of

EVmay be given in terms of the differential probabilities of ionization with energy lossbetween E and E+dE, viz EV ¼m2l

l ½EdpiðE; TÞ=dEdE=m2I

I ½dpiðE; TÞ=dEdE, where theseprobabilities are simply the ratios of the relevant ionization cross-sections to the totalenergy loss cross-section Eq (11) impressively applies for various media over a wide span

of energy, except perhaps at very low energy

Another numerical method devised by LaVerne and Mozumder [50] has been applied

to gaseous water under electron and proton irradiation Considering a small section of thetrack, the W value due to the primary particle only, may be written as xP= S(E)/Nri(E ), whereS(E ) is the stopping power, N is the molecular density, and ri(E ) is the total ionizationcross-section at energy E The number of secondary electrons produced, in all generations,per unit track length is given byNme m

I ðdri=deÞ½e=WðeÞde, where W(e) is the integral W value

for electrons at energy e, dri(e)/de is the differential cross-section for producing secondaryelectrons of energy e, and em is the maximum secondary electron energy often wellapproximated by (EI)/2 Combining, the differential x value at electron energy E is given

by xðEÞ ¼ SðEÞ=N½riþme m

I ðdri=deÞeW1ðeÞde From this equation, the overall W valuemay be calculated through integration by using the stopping power, ionization cross-section, and the integral W values obtained at lower energies A building-up principle hasbeen used by dividing the incident energy into several intervals, I–3I, 3I–7I, 7I–15I, and so

on In the first interval, no secondary ionization is possible and x(E) = xP(E), although

an integration is necessary to compute W(E) In subsequent intervals, the W(E) values ofprevious intervals may be used together with stopping power and ionization cross-sectionobtained either from experiments or tabulations By careful analysis of experiments andcompilations, LaVerne and Mozumder [50] made the following conclusions (1) Variousexperiments on the ionization cross-section are basically in agreement with each other, butthose on the excitation cross-section are not, which is the major source of uncertainty inthe calculation of W value (2) For electron irradiation, an asymptotic Wlis reached at 1keV, but the computed value (34.7 eV) exceeds measurement [51] (29.6 eV) by 15%,attributable to errors in inelastic cross-sections (3) For proton irradiation, Wlis reached

at 500 keV and the computed value (28.9 eV) is in good agreement with experiment [51](30.5 eV) In both cases, xPgreatly exceeds W, underscoring the importance of secondaryionization

Cole [52] measured the W value in air for electron energies from 5 to 20 eV, while theelectrons were completely absorbed in the ionization chamber Later, Combecher [53]extended the measurements of W(E ) to several gases including water vapor Fig 6 showsthe variation of W(E ) with electron energy in water vapor, as measured by Combecher,

theoretical calculation ( _ ) and with an empirical model (- - -) Note that the accuracy of thetheoretical calculation is limited by an inherent error in inelastic collision cross-sections, while inthe empirical model, U = 12.6 eV has been adjusted to obtain best agreement with the experiment

and compares it with the calculation of LaVerne and Mozumder and also with Inokuti’sresult, obtaining U = 12.6 eV, close to the ionization potential, for best adjustment.The effect of condensation on the W value has been treated elsewhere in some detail[54] Except for liquefied rare gases, where the W value in the liquid is somewhat less thanthat in the gas phase, there is an operational problem in the definition of W—thusrequiring long extrapolation In some hydrocarbons such as cyclohexane, the admittedlylong extrapolation of scavenging yield gives a W value not far from the level obtained inthe gas phase (f26 eV for cyclohexane) In most polar liquids, Wliq(22F 1 eV for water)

is considerably less than Wgas(31F 1 eV for water) The exact reason for the additionalyield of ionization in the liquid phase is not clear, but a significant contributing factorcould be the conversion of excited states into ionization by interaction with neighboringground state molecules in the liquid phase

As for the stopping power and the degradation spectrum, the W value is also a meanquantity and ionization fluctuation is expected because of the various ways a depositedenergy can be partitioned into ionizing and nonionizing events The Fano factor representssuch fluctuations, and it is defined as the ratio of mean square fluctuation of ionization tothe average number of ionizations, i.e., F = (hn2

iihnii2)/hnii, where nIis the number ofionizations detected in a sample For a Poisson distribution, F = 1; for other distributions,

it is <1 For the operation of a radiation detector, a smaller Fano factor means betterenergy resolution With solid state detectors using Si or Ge, Fano factors off0.05 can beachieved Other liquefied rare gas detectors have Fano factors in the rangef0.1 to f0.2

4 CONCLUSION

In this chapter, we have attempted to describe the interaction of fast charged particles withmatter from the point of view of the incident radiation, i.e., basically radiation physics Wehave discussed such topics as energy transfer from incident radiation to ionized andexcited states of medium molecules, as well as theories of stopping power and secondaryionization effects In many of the succeeding chapters, topics which are more chemical innature will be found, i.e., the response of the matter receiving the transferred energy Inthis sense, this chapter may be considered as preparatory groundwork for the succeedingcontributions

REFERENCES

FL: CRC Press, 1991, chaps 2 and 3

Wiley-Interscience: New York, 1969, chap 1

York, Vol 5,181–239

Curry, R.D.; O’Shea, K.E.; Eds.; John Wiley: New York, 1998, chap 24

York, 1968, 43–92

9 Kellerer, A.M.; Rossi, H.H In Proceedings of 2nd Symposium on Microdosimetry, Ebert, H.G.,Ed.; Euratom: Brussels, 1969, 843–853.

John Wiley: New York, 1960, 14–21

20

Press: New York, 1962, 47

Research Council: Washington, DC, 1964, (publication 1133)

York, 1980–1985, 1–6

92, 47

1971

Ionization and Secondary Electron Production

by Fast Charged Particles

as well as contributing to the discovery of x-rays and natural radioactivity With the covery of energetic alpha particles emanating from natural radioactivity, Rutherford andhis coworkers were able to investigate heavy charged-particle scattering in materials andgain new insights into the physical nature of atomic structure and of charged particlescattering These studies also stimulated new questions regarding the mechanisms of ener-

dis-gy loss by heavy charged particles in matter

The first decades of the 20th century saw great advances in our knowledge of chargedparticle interactions with matter With the discovery of nuclear fission came enhancedavailability of radionuclides and nuclear radiations, including fast fission fragments, neu-trons, alpha and beta particles Coincidently, with the development of nuclear technologycame the need to better understand the physical, chemical, and biological interactions ofradiation with matter The potential exposure of materials and people to nuclear radiationemphasized a need to understand the underlying mechanisms leading to damage by ra-diations of different types The early part of the 20th century was also a period of rapidlyexpanding technology enabling one to produce and accelerate electrons and ions and toexplore new applications of radiation in science and industry Understanding of the in-teraction of radiation with matter has important applications in numerous research andapplied fields of endeavor, including the sterilization of food and medical instruments,medical diagnosis and treatment of disease, and developments of nuclear energy and radio-active waste management (see the Preface andChap 26).In this chapter, we will explorethe fundamental mechanisms for the interaction of fast charged particles with matter, withfocus on their significance to the subsequent chemistry initiated by the absorption of ioniz-ing radiation

Ionizing radiation, as the term implies, defines those radiations that interact withmatter by the production of charged particles, namely electrons and residual positive ions

Energetic electromagnetic radiation, i.e., x-and g-rays, interact with matter predominatelyvia production of photoelectrons and Compton electrons, and, if the photon energy isgreater than about 1 MeV, the production of electron–positron pairs These primaryelectrons can have a broad spectrum of energies from subexcitation, or very slowelectrons, to what are generally called fast charged particles Here‘‘fast’’ implies particleswith velocities much larger than bound electrons of the medium As we will see, electronsand fast heavy charged particles, e.g., protons and alpha particles, predominantly interactwith the bound electrons of the medium producing secondary electrons via targetionization For completeness, we note that the interaction of neutrons with matter alsoleads to local energy deposition by charged particles; neutrons primarily interact throughelastic nuclear scattering, resulting in the production of energetic recoil charged particlescharacteristic of the absorbing medium Ionization resulting from the slowing of energeticions and electrons leads to the production of charged and/or neutral molecular fragments,reactive radicals, and other excited chemical species that foster subsequent chemicalreactivity in the absorbing medium Because all ionizing radiation leads to electronproduction, the different chemical yields observed for different types of radiation mustdepend on the detailed spatial distributions of initial events produced in the physicalprocess of electron slowing All radiation-induced chemistry begins with the stochasticphysical processes involved in energy deposition by charged particles.

Investigation of the interactions of charged particle with matter has traditionallybeen viewed as comprised of studies falling into two fundamental classes: Class I studiesfocus on the fate of the particle, and class II studies focus on the fate of the absorbingmedium [1] (cf Sec 2.1.2) The former is most commonly represented by the studies ofcharged-particle stopping powers, whereas the latter includes studies of media quantitiessuch as the average energy per ion pair (W value), or more specifically, the fundamentalprocesses of ionization and excitation that contribute to spatial structure in the patterns ofenergy deposition In the following, we will first discuss the stopping of fast chargedparticles through the general theory of stopping power, its strengths and limitations, andthen look more closely at the individual processes that contribute to energy loss and areincorporated within the general concepts of stopping power

2 STOPPING POWER

When a fast charged particle passes through matter, it loses energy by interactions volving momentum transfer to the bound electrons of the media If the particle slows tothe point that insufficient momentum can be transferred to excite these bound electrons tovacant states, energy loss will then occur through elastic collisions with the target atom, orthe target matrix, as a whole This latter energy-loss mechanism, termed ‘‘nuclear scat-tering,’’ dominates for ion energies less than a few keV per atomic mass unit (keV/u), i.e.,for ions near the extreme end of their range For high-energy or fast particles, i.e., particleswith velocities large relative to the velocities of bound electrons, inelastic collisions involv-ing electron excitation and ionization dominate the energy loss process At intermediateenergies, the competition between elastic and inelastic processes depends on the atomic,molecular, and condensed-phase properties on the absorbing medium and, for heavycharged particles, additional channels of electron capture and loss can become importantmechanisms for energy loss

in-Stopping power has been the subject of study for more than a century beginning withthe pioneering work of Thompson and Rutherford With the discovery of nuclear fission